The half-life of radioactive Technetium-99 is 6.0 hours.Find the number of ⁹⁹Tc nuclei necessary to produce a sample of activity 1.0 µCi.(1 Ci = 3.7 x 10¹⁰ decays/second)

Question

Quizplus · Accepted Answer

The activity of a radioactive sample is given by:

Activity = Decay constant x Number of radioactive nuclei

Since the activity is given as 1.0 µCi = 3.7 x 10^7 decays/second, and the decay constant for Technetium-99 is given as λ = ln(2) / half-life = ln(2) / 6.0 hours = 0.1155 hours^-1, we can solve for the number of radioactive nuclei:

1.0 µCi = (3.7 x 10^7 decays/second) = (0.1155 hours^-1) x N
N = (1.0 µCi) / (3.7 x 10^7 decays/second) x (1/0.1155 hours^-1)
N = 1.2 x 10^19 nuclei

Therefore, the answer is choice B: 1.2 x 10^19.

The Half-Life of Radioactive Technetium-99 Is 6